From d56bf4f939d25cea9ac9953b2b0f3237b2dfe8cd Mon Sep 17 00:00:00 2001
From: daHugen <david.hugentobler@ost.ch>
Date: Tue, 19 Jul 2022 18:35:13 +0200
Subject: added some equations and made some changes
---
buch/papers/lambertw/teil4.tex | 14 ++++++++++----
1 file changed, 10 insertions(+), 4 deletions(-)
(limited to 'buch/papers/lambertw')
diff --git a/buch/papers/lambertw/teil4.tex b/buch/papers/lambertw/teil4.tex
index e0f7731..6184369 100644
--- a/buch/papers/lambertw/teil4.tex
+++ b/buch/papers/lambertw/teil4.tex
@@ -237,10 +237,16 @@ Leitet man die Funktion \eqref{lambertw:funkLoes} nach x ab und setzt die Anfang
\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}
&=
\eta \\
- x\left(t\right)
- &=
- \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}} \\
\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}
&=
- \left(\frac{x}{x_0}\right)^2
+ \left(\frac{x}{x_0}\right)^2 \\
+ x\left(t\right)
+ &=
+ \sqrt{\frac{W\left(\chi\cdot e^{\chi-\frac{4t}{r_0-y_0}}\right)}{\chi}}
\end{align*}
+\begin{equation}
+ y(t)
+ =
+ \frac{1}{4}\left(\left(y_0+r_0\right)\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}+\left(r_0-y_0\right)\cdot\mathrm{ln}\ \left(\frac{W\left(\chi\cdot e^{\chi\ -\ \frac{4t}{r_0-y_0}}\right)}{\chi}\right)-r_0+3y_0\right)
+ \label{lambertw:funkNachT}
+\end{equation}
--
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